Similar triangles theorem
1. similar triangles definition:
A triangle with equal angles and proportional sides is called a similar triangles.
2. similar triangles's representation: it is represented by the symbol ""and pronounced as "similar to".
3. similar triangles's similarity rate:
The ratio of the corresponding sides of similar triangles is called similarity ratio.
4. similar triangles's preparatory theorem;
The straight line parallel to one side of the triangle intersects with the other two sides (or extension lines of both sides), and the cut triangle is similar to the original triangle.
Summary of knowledge points of similar triangles theorem in junior high school mathematics
As can be seen from the table, as long as the condition of "corresponding edges are equal" in congruent triangles's judgment theorem is changed to "corresponding edges"
Proportion "can get similar triangles's judgment theorem, that is, the analogy method in our mathematics, find out new knowledge on the basis of old knowledge, and explore ways to master new knowledge.
6. Right triangles are similar:
(1) The right triangle is divided into two right triangles by the height on the hypotenuse, which is similar to the original triangle.
(2) Two right-angled triangles are similar if the hypotenuse and one right-angled side of one right-angled triangle are directly proportional to the hypotenuse and one right-angled side of another right-angled triangle.
7. similar triangles's property theorem;
(1) similar triangles have equal angles.
(2) The corresponding sides of similar triangles are proportional.
(3) The ratio of the corresponding high line, the ratio of the corresponding middle line and the ratio of the corresponding angular bisector in the similar triangles are all equal to the similarity ratio.
(4) The perimeter ratio of similar triangles is equal to the similarity ratio.
(5) The area ratio of similar triangles is equal to the square of the similarity ratio.
8. Transitivity of similar triangles
If △ ABC ∽△ a1b1,△a 1c 1∽△a2b2c 2, then △ABC∽A2B2C2.
Related articles:
1. Summary of basic knowledge points of junior high school mathematics
2. The first mathematical knowledge point formula theorem daquan
3. Analysis of the main knowledge points of the most comprehensive test center of high school mathematics.
4. The necessary knowledge points of junior high school mathematics are summarized in the first and second chapters of junior high school mathematics.
5. Summary of the knowledge points of the fourth grade mathematical triangle.